Hey! The different forms of the word "from" have to do with the different articles used in the phrases. So, "from" translates simply to "da", and you can see the root of "da" in all of the words above. However, because you need to include the article (for example, "the" in the United States), this changes the form of the word. So, for example, because the United States would translate to "gli Stati Uniti", you are literally saying "I am from the United States," or "Vengo da gli Stati Uniti." But, to simplify this in speech, you can combine "da" and "gli" to "dagli." The same goes for the example with France, where the article is "la" in "la Francia." And in the example with England, it is again "la Inghilterra," but because "la" ends with a vowel and "Inghilterra" begins with one, the two are combined again to simplify speech. So "Vengo da la Inghilterra" becomes "Vengo dall'Inghilterra."
In short, you are essentially using the same root for "from," which is "da," but this is altered by the different masculine and feminine articles.
da gli = dagli
da la = dalla
da la Inghilterra = dall'Inghilterra or as another example dall'Argentina